A total of 1447 adults were polled before 1988 presidential election to indicate their preference; y1 = 727 supported John, y2 = 583 supported Erica, and y3 = 137 supported Giselle. The counts y1, y2, and y3 are assumed to have a multinomial distribution with sample size n and respective probabilities 1, 2, and 3.

What is the 95% credible interval for (1-2) using the theoretical method (with distribution properties)? (via integration method)